PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then
$∠ O P R : ∠ O P Q$ =.

2 : 1

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1 : 1

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1 : 2

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4 : 1

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Solution

The correct option is B $1 : 1$

Join the points OP, OQ and OR.
$In △ O P Q and △ O P R, O P = O P (common side) O Q = O R (radii of the same circle) ∠ O Q P = ∠ O R P = 90^{\circ} (Tangent is perpendicular to the radius) ∴ Δ O Q P ≅ Δ O R P (RHS congruency)$

$Hence, ∠ O P Q = ∠ O P R (C P C T)$
$\Rightarrow \frac{∠ O P R}{∠ O P Q} = \frac{1}{1} \Rightarrow ∠ O P R : ∠ O P Q = 1 : 1$

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PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then ∠OPR:∠OPQ =.

The correct option is B 1:1 Join the points OP, OQ and OR. In △OPQ and △OPR,OP=OP (common side) OQ=OR (radii of the same circle)∠OQP=∠ORP=90∘(Tangent is perpendicular to the radius)∴ΔOQP≅ΔORP (RHS congruency) Hence, ∠OPQ=∠OPR (CPCT) ⇒∠OPR∠OPQ=11⇒∠OPR:∠OPQ=1:1

PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then
$∠ O P R : ∠ O P Q$ =.